Assessment of Protein Reorientational Diffusion in Solution by nC Off-Resonance Rotating Frame Spin-Lattice Relaxation: Effect of Polydispersity COURTNEY F. MORGAN*, THOMAS SCHLEICHt, and

C. HERBERT CAINES

Departmrnt of Chemistry, University of California, Santa Cruz, California 95064

SY NOPSlS

The '"C off-resonance rotating frame spin-lattice relaxation technique is applicable to the study of protein rotational diffusion behavior in both model in vitro and in vivo systems. The original formalism of James and co-workers [(1978) J. Am. Chem. SOC. 100, 3590-35941 w a s constrained by the assumption of random isotropic reorientational motion of a monodisperse protein population. Here we extend the formalism to include polydispersity. Application is made to the alkaline pH induced association of lysozyme, lysozyme-bovine serum albumin mixtures, and to the phase separation of lysozyme salt- water mixtures induced by low temperature.

INTROD UCTlON Protein rotational reorientational motions on the time scale of 10p9-10-6 s may be conveniently monitored by employing the 13C off-resonance rotating frame spin-lattice relaxation technique introduced by James and co-workers.' The technique involves the measurement of the equilibrium magnetization in the presence ( M e ) and absence ( M ( , ) of an off-resonance radiofrequency (RF) field.'" The ratio of signal intensities ( R = M J M o ) is theoretically equal to the ratio of the off-resonance rotating frame spin-lattice relaxation time (TplfF)to the spin-lattice relaxation time (TI). The theoretical expressions for the relaxation times are formulated in terms of spectral density functions, of assumed relaxation mechanism contribution, in which the motional information (correlation time) is embedded. Thus, R can be interpreted in terms C: 1990 .John Wiley & Sons, lnc. CCC (H)O6-.~525/90/030501-07 $04.00 Biopolymers, Vol. 29 501-507 (1990) *To whom reprint requests should be addressed. 'Present address: CIBA VISION, 5000 McGinnis Ferry Road. Alpharrtta GA 30201.

of rotational motion, i.e., a rotational correlation time (7"). The technique is applicable to both model in vitro and in vivo systems for the study of macromolecular rotational diffusion behavior.'- ' For proteins, the peptide carbonyl carbon resonance is monitored since polypeptide motional dynamics are expected to be dominated by the overall particle tumbling. This assumption has been confirmed experimentally for globular proteins.5 Relaxation mechanisms pertinent to the study of proteins are typically dipole-dipole and chemical shift anisotropy (CSA), assuming either isotropic',2 or anisotropic2' reorientation. The origmal formalism' was limited b,v the assumption of random isotropic reorientation of a monodisperse protein population, thus allowing the determination of a unique value for ro. Polydispersity effects are manifested by failure to obtain a unique value of ro for different combinations of the off-resonance field strength and frequency. In this paper, we extend the formalism to include polydispersity. A companion paper' considers the case of anisotropic tumbling. Application is made to lysozyme, bovine serum albumin (BSA), lysozyme-BSA mixtures, the alkaline pH induced asso501

502

MORGAN, SCHLEICH, AND CAINES

ciation of l y s ~ z y m eand , ~ the phase separation of lysozyme salt-water mixtures induced by low temperature. The latter has been used to model the “cold cataract” occurring in the juvenile mammalian eye lens.’

lar sizes) may be treated statistically to yield different moments of the mean to achieve a single overall description of the average correlation time.9 The different moments of the mean that define the average correlation time are expressed by the following equation:

THEORY The basic features of the off-resonance rotating frame spin-lattice relaxation technique involve the polarization of nuclear spins along an effective field established by a low-power off-resonance RF field applied for a time period of a t least 3T1, followed by a hard (on-resonance) n/2 pulse to sample the z magnetization. The behavior of the spectral intensity ratio ( R = Tp:/T,) for rigid hydrodynamic particles engaged in rotational reorientational motion can be expressed by a plot of R vs we, where we is the Larmor precessional frequency about the effective field. The R vs we (frequency-dependent) dispersion curve is defined at a particular effective offresonance field strength B , , and by a rotational correlation time ro. Moreover, R can be expressed as a function of the rotational correlation time at a given value of B , and we. However, the advantage of a frequency dispersion representation of the spectral intensity ratio is that the effect of size heterogeneity, i.e., polydispersity, can be readily included. This is accomplished by taking into account the individual correlation time contributions to the overall value of R from differently sized tumbling species. Polydispersity

The effect of polydispersity on R is incorporated in the following manner: The contribution of each protein size species j is weighted by its mole fraction since this technique essentially counts the number of nuclear spins. The weighting of each species j is in turn equivalent to the weight fraction with the assumption of a mean amino acid residue molecular weight. Thus,

where f , is the weight fraction of the j t h protein species. Rotational correlation time distributions arising from polydispersity (i.e., a distribution of molecu-

where r j is the rotational correlation time of the j t h species, f, is the corresponding weight fraction, and a is a constant. When a = 0,1,2,3 .. ., the number, weight z and z + 1 average rotational correlation time, respectively, is obtained. Quantitative analysis of the R vs we dispersion curve is achieved by nonlinear least-squares regression with R and we the respective dependent and independent variables. Nonlinear regression was performed by incorporating the off-resonance rotating frame spin-lattice relaxation formalism (see accompanying paper) into the program NONLINWOOD.” The results were insensitive to the choice of the input parameters. (Copies of the programs are available upon request.) The dispersion curve is a nonlinear function of the constituent individual ro, values that define the curve. Therefore, an effective correlation time ( rO,eff)is obtained from a fit of experimental data using a model that assumes a single correlation time (i.e., monodispersity) for random isotropic reorientation. The assumption of random isotropic reorientation is reasonable for globular proteins with axial ratios less than 2.236Therefore, the obtained value of ro,eff represents an intricate average of the constituent rotational correlation times. More complex models may also be employed such as those that, for example, recognize polydispersity arising from discrete protein mixtures from an assumed model of association.

Simulations

Simulated R vs w, dispersion curves for a monodisperse protein sample as a function of molecular weight, and for polydisperse mixtures of different number average molecular weight are shown in Fig. 1(A) and Fig 1(B), respectively. To relate values of r,),rff obtained from nonlinear least-squares regression analysis (assuming monodispersity and isotropic tumbling) of simulated dispersion curves representing polydisperse mixtures

HEORIENTATIONAL DIFFUSION

503

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.-0

0.8

+.J

0

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0.6

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2x

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4x

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6x

lo4

8x

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o5

w e (rad/s) (a) I

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I

I

2 x lo4

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'

Figure 1. Simulated carbonyl 'C intensity ratio ( R ) vs we frequency-dependent plots. The computed curves assume an off-resonance field strength of 0.5 gauss and a Q, field strength of 7.05 T a l a . Dipolar relaxation by a proton 2.16 A from the I 'C and CSA relaxation mechanism contributions were assumed. Values of - 81.8 ppm and - 0.82 were used for 8, and 9,respectively.2 (A) Monodisperse as function of MW; (B) polydisperse as function of the number average molecular weight. Curve 1 (M,, = 39,623): 30 kDa (50%), 50 kDa (25%),70 kDa (25%);Curve 2 ( M , , = 39,474): 25 kDa (40%),50 kDa (40%),150 kDa (20%); Curve 3 (M,, = 45,455): 25 kDa (33%), 50 kDa (33%), 150 kDa (33%). For the calculation of T() from molecular weight, the following parameters were used: partial specific volume = 0.703 g/cm'; hydration = 0.57 g H,O/g protein; T = 35°C.

to a n average correlation time, a heuristic approach was adopted. Using the fitted values of ro,eff from simulated dispersion curves representing mixtures o f known polydispersity, the value of a in the expression defining the average correlation time was varied until the sum of the squares of [ T ~ -~ was minimized, where T ~ ~ is, defined ~ ~ , ~ by Eq. (2). This is shown in Fig. 2. The best value of a was found to be 0.56, which places the average

,

correlation time approximately midway between the number and weight averages. Use of this value of a in Eq. (2) provided a calculated average rotational correlation time within 4% of the value of T(),eff, obtained by nonlinear least-squares regression ~ analysis, ~ as described above, of representative simulated dispersion data contained in Table I. This permits reconciliation of T(),eff values with either known or assumed molecular weight distributions.

504

MORGAN, SCHLEICH, AND CAINES

10.0 9.0 8.0

'u,

7.0

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6.0 5.0 4.0 3.0 2.0 1 .o

0.0 -1.01

0.40

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0.50

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0.55

0.60

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Figure 2. a-Factor optimization. E(ql,eff 7 ) 2 vs the parameter a in Eq. (2) (see text) using the data contained in Table I. The minimum occurs a t a = 0.56. ~

Table I Correlation Times ( T ( , , + and ~ 70, c a , r ) for Simulated Polydisperse Protein Mixtures" Weight Percentage Constituent Protein 25

50

150 kDa

33 25 50 40

33 50 25 40

33 25 25 20

30

50

70 kDa

33 25 50 40

33 50 25 40

33 25 25 20

Correlation Times (ns) Ttllrff

T,; rdli

%

21.1 20.4 17.6 17.6

20.6 19.9 16.9 17.1

%

17.0 17.2 15.2 15.7

16.9 17.1 15.1 15.6

"For the calculation of 7) from molecular weight, the parameters listed in the caption of Fig. 1 were employed. "Obtained by nonlinear regression of simulated dispersion curves for assumed polydisperse protein mixtures. See text for details. 'Calculated using Eq. (2) (see text).

METHODS Sample Preparation

Lysozyme (Sigma, grade I from chicken egg white, 3 x crystallized, dialyzed, and lyophilyzed containing 90% protein) and BSA (Sigma, fraction V power containing 98-99% albumin) were used without further purification. Ionic strength was controlled by preparing all solutions from stock 1M NaC1. Dilute HCl or NaOH (ca. 0.1-0.2 N) was used to adjust the pH. After dissolving the protein in saline and adjusting the pH, the solution was centrifuged a t 300 X g for 5 min to remove air bubbles and any undissolved material. Protein concentration were

determined by absorbance a t 280 nm. Extinction coefficient values of Ei& = 26 (lysozyme)8 and 6.7 (BSA)" were used. Protein mixtures were prepared from individual lysozyme and BSA protein solutions of known concentration with the desired pH and ionic strength by mixing the two solutions in the desired proportions. In all cases total protein concentrations of ca. 100 mg/mL were employed.

NMR Measurements

All measurements were made a t 7.05 Tesla using a General Electric GN-300 spectrometer equipped with a broadband decoupler. Measurements of '"C

REORIENTATIONAL DIFFUSION

spin-lattice relaxation times ( T , ) were made with the inversion-recovery Fourier transform (IRFT) method." T h e off-resonance rotating frame spin-lattice relaxation experiment was performed using a 20-mm broadband probe as previously de-

~ c r i b e d . ' .The ~ broadband decoupler was used to provide the off-resonance B, field. Calibration of the off-resonance B, field was achieved by determining the rotational frequency of the broadband decoupler output at a given power level on a stan-

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C e, C -

+

0.4 0.2 0.0

0

lo4

2x

4x

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lo4

8x lo4

1 x lo5

Figure 3. Carbonyl "k intensity ratio ( R )vs we,plots for lysozyme (0)( T , , , ~ = . ~ 10.1 i- 0.5 ns) and BSA (0) = 22.1 f 0.8 ns), and a synthetic binary mixture of these two proteins ( 0 )(0.48 weight fraction BSA). The solid lines for the two protein preparations represent the theoretical line calculated for isotropic tumbling with the indicated best fit 7,) value, whereas for the mixture the dashed line represents the calculated curve for the best fit value of 0.45 i 0.05 weight fraction of BSA in the mixture, and the assumed 7 ) . values for the constituent pure proteins. RF field offsets from 2 to 10 kHz and a field strength of 0.4 gauss were employed. Solution conditions were 100 mg/mI, total protein concentration, 0.5M NaCl, pH 5.5, and 35°C. ~

I

I

I

I

I

I

'

I

I

I

I

I

0

2x

0 .-

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L21

x

.+ _

cn C aJ 4 c -

0.0

lo4

505

4 x lo4

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1 x lo5

Figure 4. Carbonyl '"C intensity ratio ( R )vs we plots for lysozyme a t pH value of 4.4 ( 0 )and 8.0 (0)in 0.15M NaCl a t 15°C. The solid line represents the best fit T , , , ~ , ~value of 1 I .6 0.5 ns a t pH 4.4; the dotted line represents a T,,,.~ of 21.2 i 0.6 ns a t pH 0.8. The dashed line represents the simulated dispersion curve for a lysozyme dimer ( T,) = 23.2 ns) assuming isotropic reorientation. RF field offsets from 2 to 9 kHz and a field strength of 0.5 gauss were utilized. Assuming an indefinite self-association (isodesmic) model in the analysis of R vs we yielded an apparent association constant of 66 9 L/mole.

506

MORGAN, SCHLEICH, AND CAINES

dard sample. The standard sample contained 2% (w/v) of 1 -13C enriched sodium acetate (99 atom %) at the appropriate ionic strength and ca. 35 p M MnCl, to reduce the carbonyl Tl to 6.5 s. The probe tune and match was optimized for each sample. The 13C off-resonance field strengths used were between 0.5 and 0.6 Gauss; off-resonance frequencies ranged from 2 to 30 kHz from the carbonyl resonance. All off-resonance rotating frame spectra were referenced against a control spectrum acquired at a resonance offset of 200 kHz. Typically, spectra were recorded with sweep widths of -t15 kHz and 4K data points. Quadrature phase detection and phase cycling to remove baseline artifacts were used. Between acquisitions the off-resonance field was continuously applied for approximately 3T1 (up to 18 s) of the protein carbonyl resonance. Sample temperature was regulated to within f 05°C of the desired value.

-

RESULTS AND DISCUSSION Three polydisperse systems were investigated by the off-resonance rotating frame spin-lattice relaxation technique utilizing the approach and methodology described above. The intensity ratio I

1 .o

.o

0.8

c

0

nL

.-v)

0.6

4

C

a,

+

I

L o & -

If

frequency dependent (dispersion) curves ( R vs w e ) for monodisperse lysozyme and BSA preparations under conditions favoring the monomeric state of lysozyme, and a synthetic binary mixture (0.48 weight fraction for BSA) are shown in Fig. 3. Nonlinear regression analysis of the pure lysozyme and BSA solutions, assuming isotropic reorientation, yield T ~ values , ~of 10.1 ~ 0.5 and 22.1 f 0.8 ns at 35"C, respectively. For the protein mixture, nonlinear regression analysis assuming a binary mixture model indicated a weight fraction of 0.45 0.05. These T ~ values , ~ and ~ the known weight fractions of the proteins comprising the binary mixture predict an average T value of 14.8 ns, when a = 0.56 in Eq. (a), whereas the rO,eE value obtained by nonlinear regression was 14.4 0.7 ns, a value in good agreement. The pH-induced association of l y s ~ z y m ewhich ,~ occurs at pH values greater than 5.5, was also investigated. Lysozyme was examined in 0.15M NaCl a t 15°C under monodisperse (pH 4.4) and polydisperse (pH 8.0) conditions. The intensity ratio frequency dependent curves are shown in Fig. 4. At pH 4.4, lysozyme was found to have a T ~ , value of 11.6 f 0.5 ns, but at pH 8.0 T ~increased , ~ ~ to 21.2 f 0.6 ns, indicating aggregation, and thus polydispersity. Assuming a model of indefinite

+

I

I

I

/

/ / O O

0.4

C -

0.2

0.0

Figure 5. Carbonyl l3C intensity ratio ( R )vs we plots for lysozyme in 0.5M NaCl (pH 5.5) at 35°C (0) and 1°C (0).The protein concentration was 100 mg/mL. The latter temperature induces a phase transition resulting in mimicking the cold cataract condition of juvenile mammalian eye lenses and lens protein solutions. RF field offsets from 2 to 36 kHz and a field strength of 9.55 gauss were employed. The solid line represents the best fit assuming a model of isotropic reorientation with T , , , ~=~ 7.7 k 0.4 ns a t 35°C; at 1°C the dotted line represents a T , , , , ~ of ~ 53.7 6.8 ns, using the same isotropic monodisperse model. The dashed line represents the simulated dispersion curve for a lysozyme dimer at 1°C (T,, = 41.6 ns) assuming isotropic reorientation. A nonlinear regression analysis assuming a self-association model yielded an apparent association constant of 178 k 60 L/mole.

~

~

REORIENTATIONAL 1)IFFUSION

self-association (isodesmic) in the nonlinear regression analysis of R vs we yielded an apparent association constant of 66 k 9M-', a value somewhat lower than obtained by rigorous thermodynamicbased methods at lower protein concentration^.'^ For comparison, the simulated dispersion curve for a dimer of lysozyme (7" = 23.2 ns) is included in Fig. 4. As shown in the figure this trace is a fair representation of the experimental data. Lysozyme exhibits a reversible phase separation a t 100 mg/mL, pH 5.5, and 0.5M NaCl upon cooling to below a critical temperature of ca. 5°C. Intensity ratio frequency dependent curves are shown in Fig. 5. A t 35°C nonlinear regression analysis yields a T ~ , , .value ~ of 7.7 f 0.4 ns, whereas at 1"C, using the same isotropic monodisperse model, a value of 53.7 f 6.8 ns was obtained for T " , ~ The ~ . increase in T ~ ef) , concomitant with this temperature lowering by a factor much greater than the theoretically expected value of 2.7 indicates protein association, since the additional increase in T ~ef, would require an increase in axial ratio from 1.7 to ca. 5 in the absence of association.' Application of an isodesmic self-association model, as used in the above example, provides an apparent association constant of 178 k 60M-'. The simulated trace for a lysozyme dimer, as shown in Fig. 5, represents a substantially poorer fit of the experimental data than the isodesmic model. These studies demonstrate that polydisperse protein samples can be analyzed by the off-resonance rotating frame spin-lattice relaxation technique if a model describing the molecular weight distribution is known or a reasonable one is assumed. Thus, the derived rotational hydrodynamic information is dependent upon the model employed to interpret the relaxation data. Application of the off-resonance rotating frame nmr

507

formalism, modified to include the effects of polydispersity, should prove useful for the study and characterization of protein rotational dynamics in complex biological systems.4 This research was supported by National Institutes of Health grant EY 04033.

REFERENCES 1. James T. L., Matson, G. B. & Kuntz, I. I). (1978)

J . A m . Chem. Soc. 100, 3590-3594. 2. Schleich, T., Morgan, C. F. & Caines, G. H. (1989) Methods Enzymol. 176, 386-418. 3. James, T. L., Mathews, R. & Matson, G. H. (1979) Biopolymers 18, 1763-1768. 4. Morgan, C. F., Schleich, T., Caines, G. H. & Farnsworth, P. N. (1989) Biochemistry 28,5065-5074. 5 . Bauer, D. R., Opella, S. J., Nelson, D. J. & Pecora, R. (1975) J . A m . Chem. Soc. 97, 2580-2582. 6. Morgan, C. F., Schleich, T., Caines, G. H. & Michael, D. P. (1990) Biopolymers, following paper. 7. Sophianopoulos, A. J. & van Holde, K. E. (1964) J . Biol. Chem. 239, 2516-2524. 8. Tanaka, T., Ishimoto, C. & Chylack, L. T., Jr. (1977) Science 197, 1010-1012. 9. Tanford, C. (1961) Physical Chemistry of Macromolecules, Wiley, New York, p. 145. 10. Daniel C. & Woods, F. S. (1980) Fitting Equations to Data, Wiley, New York. 11. Sober, H. A. & Harte, R. A., Eds. (1970) Handbook of Biochemistry, 2nd ed., Chemical Rubber Co., Cleveland, OH, p. C71. 12. Matson, G. B., Schleich, T., Serdahl, C., Acosta, G. & Willis, J. A. (1984) J . Magn. Reson. 56, 200-206. 13. Wills, P. R., Nichol, I,. W. & Siezen, R. J. (1980) Biophys. Chem. 11,71-82. Receiued December 7, 1988 Accepted March 17, 1989